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Four intracratonic basins of North America, the Hudson Bay, Michigan, Illinois and Williston basins, have similar ages and are close to one another. Yet, they exhibit different subsidence histories characterised by different time-scales and sediment thicknesses. They can be explained by local lithosphere thinning and by the cooling of the induced thermal anomaly. Within the framework of 1D thermal models for vertical heat transport, each basin requires a different lithosphere thickness or a different boundary condition at the base of the lithosphere. Heat flow and seismic studies show that, beneath the North American craton, the lithosphere is too thick for the assumption of purely vertical heat transfer to be valid. Thermal models are developed to account for finite thermal anomaly width and for two types of basal boundary conditions, fixed temperature or fixed heat flux. Different subsidence histories are explained by …